Finite Group DatabasebetaFinite Group Databasebeta| order | 2816 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #18284 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C11 · Schur multiplier (H2) = C25 |
| direct product | C11×#18297 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C11 | C2×#120 |
| commutator, Frattini, cosocle | C22×C4 | C24×C11 |
| prime radical | C2×C11×#538 | C2 |
| LCS | G ▷ C22×C4 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C11 ◁ C23×C4×C11 ◁ G | |
1084 conjugacy classes of subgroups.
| minimal degree | μ(G) = 43 |
| transitive degree | μt(G) = 352 |
A minimal faithful permutation representation — 4 generators on 43 points:
(1,2,3,4,5,6,7,8,9,10,11)(12,13,17,22)(14,23,26,32)(15,20,16,29)(18,21,27,35)(19,30,34,24)(25,37,38,43)(28,36,31,40)(33,41,42,39);(12,14)(13,19)(15,24)(16,30)(17,26)(18,25)(20,32)(21,33)(22,34)(23,29)(27,38)(28,39)(31,41)(35,42)(36,43)(37,40);(12,15,27,31)(13,20,35,40)(14,24,38,41)(16,18,28,17)(19,32,42,37)(21,36,22,29)(23,33,43,34)(25,39,26,30);(13,21)(19,33)(20,36)(22,35)(23,37)(29,40)(32,43)(34,42)440 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2816, 11285);